If she didn't love her why would she care so much that she thought she was a monster? I think this describes her feelings towards her mother perfectly. She hates her and yet she loves her.

Probably. I think she really loves her though, although she hates her for thinking she was a monster.

I'm pretty sure she loves her mom. However she's hates her mother for not loving her more. I think the reason she hates her mom is because she didn't feel loved by her, she hates her because she felt hated. But deep down, as exploited in the comet she does care a lot. You can tell that in The Search she was very conflicted about it the whole time, like she wanted to hurt her mother but she also didn't; there were a number of times when she could have killed her mother but hesitated and didn't do so.

I think she Azula hates her mom, and she tries to deny the fact that she loves her, but can't.

^ Agreed.